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fp_utils.cc
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fp_utils.cc
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// Copyright 2010-2018 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
#include "ortools/util/fp_utils.h"
#include <cmath>
#include "ortools/util/bitset.h"
namespace operations_research {
namespace {
void ReorderAndCapTerms(double* min, double* max) {
if (*min > *max) std::swap(*min, *max);
if (*min > 0.0) *min = 0.0;
if (*max < 0.0) *max = 0.0;
}
template <bool use_bounds>
void ComputeScalingErrors(const std::vector<double>& input,
const std::vector<double>& lb,
const std::vector<double>& ub, double scaling_factor,
double* max_relative_coeff_error,
double* max_scaled_sum_error) {
double max_error = 0.0;
double min_error = 0.0;
*max_relative_coeff_error = 0.0;
const int size = input.size();
for (int i = 0; i < size; ++i) {
const double x = input[i];
if (x == 0.0) continue;
const double scaled = x * scaling_factor;
if (scaled == 0.0) {
*max_relative_coeff_error = std::numeric_limits<double>::infinity();
} else {
*max_relative_coeff_error = std::max(
*max_relative_coeff_error, std::abs(std::round(scaled) / scaled - 1));
}
const double error = std::round(scaled) - scaled;
const double error_lb = (use_bounds ? error * lb[i] : -error);
const double error_ub = (use_bounds ? error * ub[i] : error);
max_error += std::max(error_lb, error_ub);
min_error += std::min(error_lb, error_ub);
}
*max_scaled_sum_error = std::max(std::abs(max_error), std::abs(min_error));
}
template <bool use_bounds>
void GetBestScalingOfDoublesToInt64(const std::vector<double>& input,
const std::vector<double>& lb,
const std::vector<double>& ub,
int64 max_absolute_sum,
double* scaling_factor) {
const double kInfinity = std::numeric_limits<double>::infinity();
// We start by initializing the returns value to the "error" state.
*scaling_factor = 0;
// Abort in the "error" state if max_absolute_sum doesn't make sense.
if (max_absolute_sum < 0) return;
// Our scaling scaling_factor will be 2^factor_exponent.
//
// TODO(user): Consider using a non-power of two factor if the error can't be
// zero? Note however that using power of two has the extra advantage that
// subsequent int64 -> double -> scaled back to int64 will loose no extra
// information.
int factor_exponent = 0;
uint64 sum_min = 0; // negated.
uint64 sum_max = 0;
bool recompute_sum = false;
bool is_first_value = true;
const int msb = MostSignificantBitPosition64(max_absolute_sum);
const int size = input.size();
for (int i = 0; i < size; ++i) {
const double x = input[i];
double min_term = use_bounds ? x * lb[i] : -x;
double max_term = use_bounds ? x * ub[i] : x;
ReorderAndCapTerms(&min_term, &max_term);
// If min_term or max_term is not finite, then abort in the "error" state.
if (!(min_term > -kInfinity && max_term < kInfinity)) return;
// A value of zero can just be skipped (and needs to because the code below
// doesn't handle it correctly).
if (min_term == 0.0 && max_term == 0.0) continue;
// Compute the greatest candidate such that
// round(fabs(c).2^candidate) <= max_absolute_sum.
const double c = std::max(-min_term, max_term);
int candidate = msb - ilogb(c);
if (std::round(ldexp(std::abs(c), candidate)) > max_absolute_sum) {
--candidate;
}
DCHECK_LE(std::abs(static_cast<int64>(round(ldexp(c, candidate)))),
max_absolute_sum);
// Update factor_exponent which is the min of all the candidates.
if (is_first_value || candidate < factor_exponent) {
is_first_value = false;
factor_exponent = candidate;
recompute_sum = true;
} else {
// Update the sum of absolute values of the numbers seen so far.
sum_min -=
static_cast<int64>(std::round(ldexp(min_term, factor_exponent)));
sum_max +=
static_cast<int64>(std::round(ldexp(max_term, factor_exponent)));
if (sum_min > max_absolute_sum || sum_max > max_absolute_sum) {
factor_exponent--;
recompute_sum = true;
}
}
// TODO(user): This is not super efficient, but note that in practice we
// will only scan the vector of values about log(size) times. It is possible
// to maintain an upper bound on the abs_sum in linear time instead, but the
// code and corner cases are a lot more involved. Also, we currently only
// use this code in situations where its run-time is negligeable compared to
// the rest.
while (recompute_sum) {
sum_min = 0;
sum_max = 0;
for (int j = 0; j <= i; ++j) {
const double x = input[j];
double min_term = use_bounds ? x * lb[j] : -x;
double max_term = use_bounds ? x * ub[j] : x;
ReorderAndCapTerms(&min_term, &max_term);
sum_min -=
static_cast<int64>(std::round(ldexp(min_term, factor_exponent)));
sum_max +=
static_cast<int64>(std::round(ldexp(max_term, factor_exponent)));
}
if (sum_min > max_absolute_sum || sum_max > max_absolute_sum) {
factor_exponent--;
} else {
recompute_sum = false;
}
}
}
*scaling_factor = ldexp(1.0, factor_exponent);
}
} // namespace
void ComputeScalingErrors(const std::vector<double>& input,
const std::vector<double>& lb,
const std::vector<double>& ub, double scaling_factor,
double* max_relative_coeff_error,
double* max_scaled_sum_error) {
ComputeScalingErrors<true>(input, lb, ub, scaling_factor,
max_relative_coeff_error, max_scaled_sum_error);
}
double GetBestScalingOfDoublesToInt64(const std::vector<double>& input,
const std::vector<double>& lb,
const std::vector<double>& ub,
int64 max_absolute_sum) {
double scaling_factor;
GetBestScalingOfDoublesToInt64<true>(input, lb, ub, max_absolute_sum,
&scaling_factor);
return scaling_factor;
}
void GetBestScalingOfDoublesToInt64(const std::vector<double>& input,
int64 max_absolute_sum,
double* scaling_factor,
double* max_relative_coeff_error) {
double max_scaled_sum_error;
GetBestScalingOfDoublesToInt64<false>(input, {}, {}, max_absolute_sum,
scaling_factor);
ComputeScalingErrors<false>(input, {}, {}, *scaling_factor,
max_relative_coeff_error, &max_scaled_sum_error);
}
int64 ComputeGcdOfRoundedDoubles(const std::vector<double>& x,
double scaling_factor) {
int64 gcd = 0;
for (int i = 0; i < x.size() && gcd != 1; ++i) {
int64 value = std::abs(std::round(x[i] * scaling_factor));
DCHECK_GE(value, 0);
if (value == 0) continue;
if (gcd == 0) {
gcd = value;
continue;
}
// GCD(gcd, value) = GCD(value, gcd % value);
while (value != 0) {
const int64 r = gcd % value;
gcd = value;
value = r;
}
}
DCHECK_GE(gcd, 0);
return gcd > 0 ? gcd : 1;
}
} // namespace operations_research